...and they did. David Moyes can afford to smile a little after his United side got noticeably stronger over 90 minutes. That's not happened enough times this season...
As long as there is both football and human weakness, there will be allegations of match-fixing. But a decent start would be an independent, national body...
* Despite its billing as an unlikely top-of-the-table clash at the start of November, Arsenal's win over Liverpool ended with only one team proving their credentials in this season's title race. The Gunners may have a long way to go to hold off the challenge of Chelsea, Man City and Man United (?), but Liverpool's route back to the top is much more arduous. "I believe we are in a good place at the moment, but it will take time," said Brendan Rodgers this week, and there is no shame in the manager's admission nor in his team's 2-0 defeat on Saturday. The height of Liverpool's immediate ambition is to return to the top four, and that is a far more achievable aim following an impressive start to the campaign. They now need to brush themselves down, prepare for a home banker against Fulham next week and get back to 'churning out wins'.
* But what of Arsenal and Arsene Wenger's claim that they are genuine title contenders? The manager made a similar statement at the start of last season, despite performances and results to the contrary, but his words now carry far more weight as the Gunners stretch five points clear at the top. It was important to bounce back against Liverpool after consecutive home defeats to Borussia Dortmund and Chelsea, and Arsenal proved their quality, released the handbrake and achieved all of the manager's other oft-repeated demands.
The question of whether the Gunners can maintain their title challenge will depend on how their small squad copes with the busy winter schedule and beyond, with fears of a spring collapse already mounting in supporters' minds.
"What we want first is to convince everybody that we can play at the top and hopefully in April we can ask ourselves have we got enough resources to cross the line," said Wenger this week. It's safe to say that Arsenal have done enough convincing, while the manager's secondary aim should be aided by another foray into the transfer market at the start of January. A back-up striker remains a priority.
* While both Arsenal's goals came from the wide areas - a growing trend for the Gunners this season - the match was won in the middle, where they dominated possession and imposed their quality firstly against Liverpool's central trio and again in the second half when Rodgers switched to a 4-4-2 formation. After the successive home defeats to Dortmund and Chelsea, Arsenal finally managed to play their own game against an opponent less adept at counter-attacking.
Indeed, the Gunners found the same little pockets of space in the middle that Dortmund exploited so ruthlessly in their 2-1 victory at the Emirates to create numerous chances to burst into the penalty box. The cute link-up play between Olivier Giroud and Mesut Ozil was a defining feature of the first half as Arsenal attacked at will and forced Liverpool into switching formations as they chased the game after the break.
* As Arsenal stretched Liverpool in the first half, it may have seemed like Rodgers made the wrong decision to stick with his 3-5-2 system, but the hosts' controlled performance after the break proved that Liverpool were always going to struggle against a superior opponent brimming with confidence. However, could Rodgers have picked a slightly stronger starting line-up for his biggest test of the campaign thus far?
The big selection news before kick-off was Rodgers' decision to call on John Flanagan for his first appearance of the season - and only his third in all competitions since the end of 2011/12 - as Glen Johnson missed out through illness. The 20-year-old's sudden promotion to first-team duty underlined the manager's desire to stick with 3-5-2, which he deployed for the first time following the Reds' first defeat at home to Southampton.
Far from being a knee-jerk reaction to that disappointing loss, Rodgers' plan to play with wing-backs suits many of Liverpool's strengths, but the benefit is questionable when he is forced to select a rookie in a conflict between positional advantage and the personnel available. It would have offered Liverpool more balance if Jordan Henderson had played in the right wing-back role - as he did against Man United in the League Cup and away to Sunderland - but Rodgers' intention was clearly to overload central midfield to disrupt Arsenal's rhythm and the significant threat of Ozil and Aaron Ramsey.
As it turned out, even with three men in the centre Liverpool failed to get to grips with Arsenal's rampant midfield and it was only in the last quarter of the game that they enjoyed a sustained spell of pressure.
* Had Philippe Coutinho been fit to start, Rodgers would likely have played Henderson on the right and brought the Brazilian into the middle. However, Coutinho's erratic performance in the second half proved that it will take him time to reach full speed following the shoulder injury that ruled him out for six matches.
As an aside, why was Joe Allen not deemed worthy of a starting spot in the middle to allow Henderson to play ahead of Flanagan on the right? Rodgers has made several shrewd acquisitions during his short reign as Liverpool manager, but the £32million spent on Allen, Fabio Borini and Iago Aspas has been as useful as Kenny Dalglish's £35million outlay on Andy Carroll.
* After Arsenal were outclassed by Chelsea on Tuesday, I questioned whether Wenger could recreate the balance the injured Mathieu Flamini provides in midfield and the manager passed this particular test with flying colours. Whatever 'flying colours' happen to be.
Mikel Arteta was clearly tasked with sitting and breaking and giving, and he excelled in all three responsibilities as Ramsey was allowed to push forward and demonstrate his talent in the final third. With Jack Wilshere missing along with Flamini, Wenger's selection was made rather more easy, and the England international's absence was barely noticeable.
* It seemed as though Liverpool would be able to get a foothold in the game in the first 15 minutes through their aggressive pressing, but the key moment of the first half saw more than one player in a white shirt fail to fulfil their duties. As Arsenal attacked down the right, Flanagan and Steven Gerrard failed to track Santi Cazorla in the centre and the Spaniard was allowed two bites of the cherry to score the opener. While Kolo Toure was left to look like a fool by Giroud's typical run to the front post, at least he was in position - Mamadou Sakho, on the other hand, could be seen sauntering back without a care in the world as Cazorla's sweet strike gave Arsenal the lead.
* How Liverpool will rue Martin Atkinson's decision to prevent them taking a quick free-kick at 1-0. After Luis Suarez had been dragged down by Bacary Sagna, the striker jumped to his feet to play in Daniel Sturridge down the left but, with Henderson waiting unmarked in the middle, the referee called Liverpool back so that he could book the Arsenal defender. It would certainly have been fairer to allow the Reds to continue so that they could profit fully from Sagna's indiscretion.
* Sagna's tactical foul may have been a necessary evil to maintain Arsenal's lead, but Wenger should be worried about his team's vulnerability from their own attacking set-pieces. The Gunners have been picked off on breaks from their own corners against Aston Villa and Chelsea this season, while Arteta was red carded following a similar situation at Crystal Palace.
"People are saying this team is too open and that we cannot win things this way," said the Spaniard this week. "But it's part of our game and we want to play with risks."
There's playing with risks and then there's playing silly beggars.
* Arteta also claimed it was a "pity" that Arsenal failed to sign Suarez in the summer, but one wonders whether the club's fans share the midfielder's sentiment. There was a loud chorus of boos - enough to satisfy Andrey Arshavin, at least - when the striker was fouled by Laurent Koscielny in the opening stages as Suarez maintained his reputation as the Premier League's pantomime player.
* While Suarez and Sturridge were typically lively and threatened Arsenal's defence on several occasions, their performances strengthened the school of thought that rather than being a deadly partnership, they are two highly-skilled in-form individuals who occasionally meet on the same wavelength. There have of course been times when one has directly assisted the other - such as Sturridge for Suarez in the win at Sunderland and vice-versa in the 2-2 draw at Newcastle - but Liverpool's last two outings show that each striker's game more focused on playing selfishly rather than constantly seeking to support the other. This is not to say that there is anything wrong with the way the duo work, but one wonders how Liverpool will respond when one - probably Sturridge - suffers a dip in form. Will Suarez be the catalyst to spur on his teammate? It's likely that he wouldn't be hugely concerned.
* How poor was Aly Cissokho in his 45 minutes on the pitch? That Flanagan was preferred in the second half says much about the left-back's display and, despite not being his biggest fan, Rodgers must look forward to Jose Enrique's return from a knee injury.
* A quick word on Simon Mignolet, who demonstrated his strengths and weaknesses in a nervous display. The keeper is undoubtedly an excellent shot-stopper - the minimum requirement of a goalkeeper - but again lacked confidence with the ball at his feet, and with the ball in the air as he dropped a simple cross that almost presented Arsenal with a chance to score. For £9million-ish, the Belgian really doesn't seem to be much of an upgrade on Pepe Reina. Plus, Reina became the first man to save a Mario Balotelli penalty earlier this season, so that pretty much makes him a god in the land of goalkeepers.
* If we're having a quick word on Mignolet, it's only fair that the same is given to Wojciech Szczesny, who has been much-improved this season after he was dropped in March and April following a spell of poor form.
"Looking back now it was a good lesson for me, one that I needed at the time," said the keeper in October. "I definitely have got sharper since then, I have worked harder in training and it worked back then for me and I have carried on doing it. I am feeling like I am a bit more consistent at the moment."
His commanding performance that helped stem Liverpool's hopes in the second half highlighted why the 23-year-old is deserving of his new four-year deal.
*Jordan Henderson can't shoot for toffee, proven by the result of his early meander into the Arsenal box. Ten strikes in just over two full seasons may not seem a poor return, but considering some of the positions the 23-year-old manages to get himself into, he should really improve that tally.
He needs to fix that gait as well.
* An apology to Olivier Giroud, which is perhaps somewhat overdue. After repeatedly criticising the striker in Winners and Losers last season, he has certainly proved me wrong at the start of this campaign and some of his touches around the edge of the box - particularly in the first half - were exquisite. Wenger has been getting much more out of that side of Giroud's game this year - largely owing to Ozil's arrival - with the Frenchman proving that he is more than merely a poor finisher, which is still arguably the best description for his contribution in 2012/13.
Matt Stanger - he's on the Twitter.